BODMAS

BODMAS is a helpful acronym meaning brackets, order, division, multiplication, addition and subtraction, ensuring that equation steps are completed in the right order. A mathematical question with multiple operations may give different answers depending on the order in which it is solved.

Order of Operations - BODMAS

Operations

"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number, it is probably an operation.

But, when you see something like...

7 + (6 × 5² + 3)

... what part should you calculate first?

Start at the left and go to the right?
Or go from right to left?

Calculate them in the wrong order, and you will get a wrong answer!

So, long ago people agreed to follow rules when doing calculations, and they are:

How Do I Remember It All ...? BODMAS!

B	Brackets first
O	Orders (i.e. Powers and Square Roots, etc.)
DM	Division and Multiplication (left-to-right)
AS	Addition and Subtraction (left-to-right)

Examples

Example: How do you work out 3 + 6 × 2 ?

Multiplication before Addition:

First 6 × 2 = 12, then 3 + 12 = 15

Example: How do you work out (3 + 6) × 2 ?

Brackets first:

First (3 + 6) = 9, then 9 × 2 = 18

Example: How do you work out 12 / 6 × 3 / 2 ?

Multiplication and Division rank equally, so just go left to right:

First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3

Oh, yes, and what about 7 + (6 × 5² + 3) ?

7 + (6 × 52 + 3)
7 + (6 × 25 + 3)	Start inside Brackets, and then use "Orders" First
7 + (150 + 3)	Then Multiply
7 + (153)	Then Add
7 + 153	Brackets completed, last operation is add
160	DONE !

BODMAS

We must always add, subtract, multiply or divide the numbers in the correct order. The convention that you must follow is often called BODMAS

Work out brackets first             B

Other       (e.g. powers x²)          O

Divide                                         D

Multiply                                      M

Add                                            A

Subtract                                    S

Example 1

8 + 12 ÷ 4        =

8 + 3        = 11

not 20 ÷ 4       = 5

Example 2

10 + (8-6) x 5 =

Deal with the brackets first 8 – 6 = 2

So the question becomes 10 + 2 x 5

Then multiply 2 x 5 next = 10

Leaving 10 + 10 = 20

Worksheet

Calculate these without a calculator (take care to use the right order)

a.    5 + 2 x 7 =

b.   10 – 2 x 5 =

c.    6 x 3 + 2 =

d.   10 + 12 ÷ 2 =

e.   20 – 8 ÷ 2 =

f.    (20 – 8) ÷ 2 =

g.   2 x (5 + 7) =

h.   2 x (3 + 7 + 1) =

i.     5 x 4 – (6 – 3) =